What is the integral of 300e^{500t} ?

The integral of 300e^{500t} is 3/5 e^{500t}+C

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integral of 300e^{500t}

\int 300 e^{500 t} d t

\frac{3}{5} e^{500 t} + C

Solution steps

\int 300 e^{500 t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 300 \cdot \int e^{500 t} d t

Apply u-substitution

= 300 \cdot \int e^{u} \frac{1}{500} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 300 \cdot \frac{1}{500} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 300 \cdot \frac{1}{500} e^{u}

Substitute back

u = 500 t

= 300 \cdot \frac{1}{500} e^{500 t}

Simplify

300 \cdot \frac{1}{500} e^{500 t} : \frac{3}{5} e^{500 t}

= \frac{3}{5} e^{500 t}

Add a constant to the solution

= \frac{3}{5} e^{500 t} + C

What is the integral of 300e^{500t} ?
The integral of 300e^{500t} is 3/5 e^{500t}+C